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A Factorization Formula for Class Number Two

✍ Scribed by Scott T. Chapman; Jeremy Herr; Natalie Rooney

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
125 KB
Volume
79
Category
Article
ISSN
0022-314X

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✦ Synopsis

Let R be an atomic integral domain. R is a half-factorial domain (HFD) if whenever x 1 } } } x n = y 1 } } } y m for x 1 , ..., x n , y 1 , ..., y m irreducibles of R, then n=m. A well known result of L. Carlitz (1960, Proc. Amer. Math. Soc. 11, 391 392) states that the ring of integers in a finite extension of the rationals is a HFD if and only if the class number of R is less than or equal to 2. If R is such a ring of integers with class number 2, then we use some simple Krull monoids to develop a formula for counting the number of different factorizations of any integer x into products of irreducible elements of R.

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